As part of that course, we were given a chunk of time to sit down and write our mathematical biographies. I wrote one that day, too. I have it saved, and it will be worth sharing. It was a story of ups and downs and all the moments I learned new things (or didn't).
In writing it, I found myself knowing the punchline of the biography prior to the parable: for much of my life, I was somewhat ashamed to tell people I studied advanced mathematics . And the farther I had gotten into studying math, the more I resisted telling people, especially those I wanted to actually be my friends. It's been tricky--especially since I did abandon my study of advanced mathematics once I spent several years not progressing at my thesis problem--to figure out what that shame meant. Why was I hiding?
I came across the biography at the end of 2017. I was trying to find some notes and research from the course. And I couldn't resist myself. I returned to the first few sentences, which I did not change. I can't exactly tell you how much of the rest is from "the original", but I doubt it's much. What I know is that my story here--a little too sore though it may be--shows itself even though the narrative has mostly disappeared.
Consider this chapter one of who I am and what issues I'm curious about mathematically. Installment 2 is likely but a few months away....
Mathematics keeps renewing itself for me
and uncovers new corners of the identities and cognitions of those around
us. I can learn so much from how others
think about or speak mathematics, and I never cease to be fascinated by the
relationship between something which is supposed to be objective, and all the
subjectivity and affect that comes to bear in its use, and how it develops.
Mathematics to me is
a culture, one into which I don't totally fit. There is a way of saying things
and writing them. I remember being very good at acquiring a mathematical style
and working through the hard problems for as long as I can remember. When mathematical
writing is good, it has a personality and style, and I appreciate trying to
mimic it.
Mathematics also can
be overwhelming. Pages of symbols moving in circles. A question that seems like
it should have an answer but does not. Discussions in which I hear someone
repeating the same phrase over and over, trying the same or multiple approaches,
and I just cannot get it.
Mathematics is this
bizarre space between intuition and application. Often I can do the first and
not the second. But when it comes to the stuff I teach, I relish in seeing more
depth and I spend my days seeing more connections. Every day a new corner of
how ideas relate and can be expressed comes forward.
Mathematics was
reinvigorated for me when I started working with teachers and seeing something
other than "definition chasing" and a challenge of my own thinking
abilities and understanding in its application.
Mathematics was
reinvigorated for me when I learned new pedagogies such as inquiry based
learning and flipped classroom learning, where more space was made open for us
to talk about how we think about things and the implications of those ideas.
My anchor to loving
math is not in being good at it, but in uncovering those people who think about
it. First Alice's Adventures in Wonderland
and logic puzzles, then Fantasia Mathematica and other short stories that took mathematical ideas and let them play with
reality--or bend it--then A Tour of the Calculus, where someone else was waxing poetic about where they saw
mathematics show up in the world, and what the people who codified Calculus
were like. Those ideas that fit together so neatly--they were quite something.
The truths that never break. You can count on them. But then I discovered in
grad school how wild things can be when you intentionally bend them.
Nonassociative groups. Topologically
nonorientable spaces. Positive scalar curvature. Alternative logical frameworks.
Something was
exciting about it, but so much more was defeating.
I don't think I'm
alone in coming to mathematics thinking there's a way to ground myself in all
of it. I must have believed that because I knew it was specifically my task.
Don't get me wrong; I knew you could always make up new problems and
definitions and take a spin on things. I was the kid who created my own games
and universes and clubs, so setting up some rules and playing was definitely my
kind of universe. I also adored off the wall improvisational theatre, and
played a good deal of "Freeze Frame" in my middle and high school
drama club days. But I think I really thought there was some stack of core
understanding of mathematical knowledge, or some set of guiding principles
which I did not fully know yet, but if only I did, then everything would put
itself together and I would never be afraid or intimidated by a problem again.
I thought there was a way, through mathematics, to have a compass to face any
problem for which it was a tool. Just read enough of its "Bible",
study it for long enough to be able to state its doctrine, and I would feel at
peace. I would have filled that nagging sense that I wasn't enough in this area
that I adored.
I should have known
better.
On one hand, I
should have known myself better. The nagging sense I wasn't enough was not
coming from not knowing mathematics. It wasn't coming from seeing people or
ideas I wanted to be like or a part of. A field doesn't do that. Facts don't do
that. The problem was I was confounding--or rather selectively applying an
identification between--the mathematical concepts, techniques, and
applications, and the people who made up and live and breathe and define what
is officially "mathematics." One cannot just learn "enough"
of a subject and be a mathematician in the way I felt myself wanting to be; one
has to take on some set of dispositions, and more importantly to my naïve self,
be taken in. I wanted to belong. The enough
was to say that who I was and loved being could intersect with this beautiful
world of ideas and solutions and analysis that had also inspired people before
me to write and share and act in ways I admired.
I so wanted to be a
Vi Hart type without knowing if I was Vi Hart. I wanted to be a John Milnor
without knowing if I was a John Milnor. I wanted to write like Gardner or
Borges or Berlinski about ideas I loved and the places they could take you,
even knowing that was not my talent. I wanted to be right, perfect, wonderful,
so that people would love me for who I was, but in wanting that I could not see
that I did not love who I was. Being the mathematical misfit is not a badge of
honor one wears out of pride when one pities the misfit and knows their pain.
It's a badge one wears out of shame.
I remember being
angry when I learned Danica McKellar had gotten into mathematics and written a
book to inspire girls. Did this mean I had done everything wrong? That it was
that I wasn't beautiful or professional enough to have followed my soul first
and done math my way? And why couldn't I just be happy that she had a voice
whom people were listening to, who might be able to change things for future
generations?
I also should have
known better because I was a child of academics. I saw all the discourses that
went into the subject which fell outside of what the facts were. I knew how
slow cultures were to change, how systems could isolate and bully and be
resistant to change even while celebrating the dispassionate and objective
pursuit of truth. I knew that the keepers of the heart of mathematics, in the
eyes of the civilized world at any rate, were tenured mathematicians who, no
matter how much they loved that which they studied and embraced it with joy,
were conscious perpetrators of an intellectual and social hazing and
acculturation of others to what they believed was right, which just like a
church governing a religion, held its greatest authority in who said it was
right, and not in what good it could do. And that hazing had to one extent or
another impacted every high, middle, and elementary mathematics teacher, thus
reinforcing its cold values on nearly every child in this country. What I had
loved about math was learning through reading that it wasn't just rules and
meeting expectations, without realizing that the rules and expectations which
still existed were equally oppressive, and that the keepers of math were the
only ones who could substantively change these misconceptions.
to be continued.
